To what extent can I extrapolate my guitar string knowledge to bass?
it's not that easy. it depends obvously on what you like and what you need.
I'm a long time user of Thomastik Jazz Flats on my Precision Bass (and even other basses), they are my favourite strings for sound, tension, balance string-to-string and whatever
here's a sample of how they sound after four years of extra-intense use:
on one of my guitars (Epiphone G400 modded with EMG 85 pickups) I've tried both Chromes 013 and Thomastik Jazz Flats 012. first of all I have to tell you that I don't play jazz music, not even close

in the bands where I play guitar we play rock/pop music, lots of effect and distortions...
I decided to try flats after reading that the guitarists from The Strokes both use Thomastik flats (they use the George Benson signature 012... but I didn't buy them, being 30 euros a set...), and loving their tone, I wanted to try flats on guitar.
Chromes were too bright and tight, and they sound exactly how they sound on bass, brighter than ususal flatwound. I didn't like them much, and even if they were 013, I broke the high-E string... (I NEVER break strings on my guitars!)
Thomasitk were heaven to my taste, warm and woody, soft to the touch. the only thing I complained was that the B and high-E are brass-plated, and in a couple of days they turned black and "rough". I know that TI makes a set with tin-plated plain strings, but I couldn't find them in shops here in Italy.
they sounded like this (I recorded these samples just to share how they sound "clean")
bridge pickup- both pickup - neck pickup. Jazz III Dunlop black pick:
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here same pickup sequence, fingers:
here, fingers, neck pickup, Stairway to heaven:
stairway, bridge pickup:
stairway, both pickups:
stairway, both pickups, in a "jazzy" way (forgive me! ahah)
to my ears they sounded and felt identical to the bass set, and I loved their tone, in particular with overdriven sounds, they were tick and rich, a mellow-hot-creamy tone cutting through the mix like no other.
I had to replace them with Elixir strings due to the fact that I needed long-lasting plain strings. I couldn't stand the fact that they were oxidised and rough. Elixir use anti-rust on their plain strings, so after an year and a half they still shine.
I'm considering to try them on my Squier Classic Vibe Stratocaster, however
so, I can say that the philosophy behing strings is pretty much the same both for guitar and bass strings, inside the brand.